Problem: If $A:B:C = 2:1:4$, what is the value of $(3A + 2B) \div (4C - A)$? Express your answer as a common fraction.
Explanation: Suppose that $B = x$.  Then $A = 2x$ and $C = 4x$.  Thus $(3A + 2B)\div (4C - A) = \frac{8x}{14x} = \frac{8}{14}=\boxed{\frac{4}{7}}$.